ELECTROMAGNETIC INDUCTION IN FINITE THIN SHEETS

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Abstract
The problem of electromagnetic induction in a uniformly conducting thin sheet in the form of a circular disk or an infinite plane with a circular hole is formalized in terms of dual integral equations. The exact solution for a perfectly conducting sheet when the inducing field is a magnetic dipole situated on the axis is found. The Fredholm integral equation giving the density of the induced currents in a thin conducting spherical cap is shown to reduce to that for a thin circular disk when the sheets are perfectly conducting, and the solution is thus found. It is shown that the solution can also be found when the conductivity is finite and has a special distribution depending on the inducing field.

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